13 citations · 57 across the 26 of their papers we have counts for
27 papers
Global well-posedness for a time-fractional doubly nonlinear equation
Goro Akagi, Giacomo Enrico Sodini, Ulisse Stefanelli
We consider a time-fractional parabolic equation of doubly nonlinear type, featuring nonlinear terms both inside and outside the differential operator in time. The main nonlinearit…
Time-fractional gradient flows for nonconvex energies in Hilbert spaces
Goro Akagi, Yoshihito Nakajima
This article is devoted to presenting an abstract theory on time-fractional gradient flows for nonconvex energy functionals in Hilbert spaces. Main results consist of local and glo…
Existence of distributional solutions to degenerate elliptic systems for locally integrable forcing
Goro Akagi, Hiroki Miyakawa
This paper presents an existence result and maximal regularity estimates for distributional solutions to degenerate/singular elliptic systems of -Laplacian type with absorption…
Energy solutions of the Cauchy-Dirichlet problem for fractional nonlinear diffusion equations
Goro Akagi, Florian Salin
The present paper is concerned with the Cauchy-Dirichlet problem for fractional (and non-fractional) nonlinear diffusion equations posed in bounded domains. Main results consist of…
Weighted Energy-Dissipation approach to semilinear gradient flows with state-dependent dissipation
Goro Akagi, Ulisse Stefanelli, Riccardo Voso
We investigate the Weighted Energy-Dissipation variational approach to semilinear gradient flows with state-dependent dissipation. A family of parameter-dependent functionals defin…
Weighted Inertia-Dissipation-Energy approach to doubly nonlinear wave equations
Goro Akagi, Verena Bögelein, Alice Marveggio +1
We discuss a variational approach to doubly nonlinear wave equations of the form . This approach hinges on the minimization of a parameter-depende…
Fractional Dissipative PDEs
Franz Achleitner, Goro Akagi, Christian Kuehn +4
In this chapter we provide an introduction to fractional dissipative partial differential equations (PDEs) with a focus on trying to understand their dynamics. The class of PDEs we…
Optimal rate of convergence to nondegenerate asymptotic profiles for fast diffusion in domains
Goro Akagi, Yasunori Maekawa
This paper is concerned with the Cauchy-Dirichlet problem for fast diffusion equations posed in bounded domains, where every energy solution vanishes in finite time and a suitably…
On a class of doubly nonlinear evolution equations in Musielak-Orlicz spaces
Goro Akagi, Giulio Schimperna
This paper is concerned with a parabolic evolution equation of the form , settled in a smooth bounded domain of , , and complemented with th…
Evolution equations with complete irreversibility and energy conservation
Goro Akagi, Kotaro Sato
This paper is concerned with the initial-boundary value problem for an evolutionary variational inequality complying with three intrinsic properties: complete irreversibility, unil…
Space-time homogenization problems for porous medium equations with nonnegative initial data
Goro Akagi, Tomoyuki Oka
This paper concerns a space-time homogenization limit of nonnegative weak solutions to porous medium equations. In particular, the so-called homogenized matrix will be characterize…
Rates of convergence to non-degenerate asymptotic profiles for fast diffusion via energy methods
Goro Akagi
This paper is concerned with a quantitative analysis of asymptotic behaviors of (possibly sign-changing) solutions to the Cauchy-Dirichlet problem for the fast diffusion equation p…
General framework to construct local-energy solutions of nonlinear diffusion equations for growing initial data
Goro Akagi, Kazuhiro Ishige, Ryuichi Sato
This paper presents an integrated framework to construct local-energy solutions to fairly general nonlinear diffusion equations for initial data growing at infinity under suitable…
Space-time homogenization for nonlinear diffusion
Goro Akagi, Tomoyuki Oka
The present paper is concerned with a space-time homogenization problem for nonlinear diffusion equations with periodically oscillating (in space and time) coefficients. Main resul…
Local well-posedness for Frémond's model of complete damage in elastic solids
Goro Akagi, Giulio Schimperna
We consider a model for the evolution of damage in elastic materials originally proposed by Michel Frémond. For the corresponding PDE system we prove existence and uniqueness of a…
Traveling wave dynamics for Allen-Cahn equations with strong irreversibility
Goro Akagi, Christian Kuehn, Ken-Ichi Nakamura
Constrained gradient flows are studied in fracture mechanics to describe strongly irreversible (or unidirectional) evolution of cracks. The present paper is devoted to a study on t…
Porous medium equation with a blow-up nonlinearity and a non-decreasing constraint
Goro Akagi, Stefano Melchionna
The final goal of this paper is to prove existence of local (strong) solutions to a (fully nonlinear) porous medium equation with blow-up term and nondecreasing constraint. To this…
Allen-Cahn equation with strong irreversibility
Goro Akagi, Messoud Efendiev
This paper is concerned with a fully nonlinear variant of the Allen-Cahn equation with strong irreversibility, where each solution is constrained to be non-decreasing in time. Main…
Convergence of solutions for the fractional Cahn-Hilliard system
Goro Akagi, Giulio Schimperna, Antonio Segatti
This paper deals with the Cauchy-Dirichlet problem for the fractional Cahn-Hilliard equation. The main results consist of global (in time) existence of weak solutions, characteriza…
The Cauchy problem for the Finsler heat equation
Goro Akagi, Kazuhiro Ishige, Ryuichi Sato
Let be a norm of and the dual norm of . Denote by the Finsler-Laplace operator defined by $Δ_Hu:=\mbox{div}\,(H(\nabla u)\nabla_ξH(\nabla u))$. In th…
Elliptic-regularization of nonpotential perturbations of doubly-nonlinear gradient flows of nonconvex energies: A variational approach
Goro Akagi, Stefano Melchionna
This paper presents a variational approach to doubly-nonlinear (gradient) flows (P) of nonconvex energies along with nonpotential perturbations (i.e., perturbation terms without an…
Quantitative estimates on localized finite differences for the fractional Poisson problem, and applications to regularity and spectral stability
Goro Akagi, Giulio Schimperna, Antonio Segatti +1
We establish new quantitative estimates for localized finite differences of solutions to the Poisson problem for the fractional Laplace operator with homogeneous Dirichlet conditio…
Stability of non-isolated asymptotic profiles for fast diffusion
Goro Akagi
The stability of asymptotic profiles of solutions to the Cauchy-Dirichlet problem for Fast Diffusion Equation (FDE, for short) is discussed. The main result of the present paper is…
Fractional Cahn-Hilliard, Allen-Cahn and porous medium equations
Goro Akagi, Giulio Schimperna, Antonio Segatti
We introduce a fractional variant of the Cahn-Hilliard equation settled in a bounded domain of and complemented with homogeneous Dirichlet boundary conditions of solid ty…